Cari amici vi invito a partecipare al seminario di Max Fathi (Università di Parigi Jussieu) presso il dipartimento di matematica dell'università di Roma La Sapienza (sito in piazzale Aldo Moro 5, Roma), i cui dettagli sono riportati di seguito. A presto Mauro Mariani

Data ed aula: lunedì 11 maggio, ore 14:30, aula di consiglio (primo piano)

Titolo: A gradient flow approach to large deviations for diffusion processes

Sunto: In the 80s, De Giorgi introduced the notion of abstract gradient flows, which allowed to define a notion of solutions to ordinary differential equations of the form x' = −grad F(x) on metric spaces (rather than Riemannian manifolds for the usual definition). In 2005, Ambrosio, Gigli and Savare showed that when we consider the space of probability measures on R d endowed with the Wasserstein metric, this notion allows to give an alternate formulation for Fokker-Planck equations. These equations are the PDEs whose solutions are the flow of marginals of solutions of stochastic differential equations of the form dX = −grad H(X)dt + dB . In this talk, I will explain how we can use this notion to study large deviations for sequences of SDEs. The main result is that proving a large deviation principle is equivalent to studying the limit of a sequence of functionals that appear in the abstract gradient flow formulation for Fokker-Planck equations. As an application, I will show how to obtain large deviations from the hydrodynamic scaling limit for a system of interacting continuous spins in a random environment.